On 1-bend Upward Point-set Embeddings of $st$-digraphs
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911749419040768 |
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| author | Di Giacomo, Emilio Förster, Henry Kokhovich, Daria Mchedlidze, Tamara Montecchiani, Fabrizio Symvonis, Antonios Villedieu, Anaïs |
| author_facet | Di Giacomo, Emilio Förster, Henry Kokhovich, Daria Mchedlidze, Tamara Montecchiani, Fabrizio Symvonis, Antonios Villedieu, Anaïs |
| contents | We study the upward point-set embeddability of digraphs on one-sided convex point sets with at most 1 bend per edge. We provide an algorithm to compute a 1-bend upward point-set embedding of outerplanar $st$-digraphs on arbitrary one-sided convex point sets. We complement this result by proving that for every $n \geq 18$ there exists a $2$-outerplanar $st$-digraph $G$ with $n$ vertices and a one-sided convex point set $S$ so that $G$ does not admit a 1-bend upward point-set embedding on $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On 1-bend Upward Point-set Embeddings of $st$-digraphs Di Giacomo, Emilio Förster, Henry Kokhovich, Daria Mchedlidze, Tamara Montecchiani, Fabrizio Symvonis, Antonios Villedieu, Anaïs Computational Geometry We study the upward point-set embeddability of digraphs on one-sided convex point sets with at most 1 bend per edge. We provide an algorithm to compute a 1-bend upward point-set embedding of outerplanar $st$-digraphs on arbitrary one-sided convex point sets. We complement this result by proving that for every $n \geq 18$ there exists a $2$-outerplanar $st$-digraph $G$ with $n$ vertices and a one-sided convex point set $S$ so that $G$ does not admit a 1-bend upward point-set embedding on $S$. |
| title | On 1-bend Upward Point-set Embeddings of $st$-digraphs |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2401.03226 |